Optical filters affecting color vision in a desired manner and design method thereof by non-linear optimization

ABSTRACT

The invention generally relates to optical filters that provide regulation and/or enhancement of chromatic and luminous aspects of the color appearance of light to human vision, generally to applications of such optical filters, to therapeutic applications of such optical filters, to industrial and safety applications of such optical filters when incorporated, for example, in radiation-protective eyewear, to methods of designing such optical filters, to methods of manufacturing such optical filters, and to designs and methods of incorporating such optical filters into apparatus including, for example, eyewear and illuminants.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Patent ApplicationNo. PCT/US2016/021399 filed Mar. 8, 2016 and titled “Optical FiltersAffecting Color Vision In A Desired Manner And Design Method Thereof ByNon-Linear Optimization”. PCT/US2016/021399 claims benefit of priorityto U.S. Provisional Patent Application No. 62/133,207 titled “OpticalFilters Affecting Color Vision In A Desired Manner And Design MethodThereof By Non-Linear Optimization” filed Mar. 13, 2015. BothPCT/US2016/021399 and 62/133,207 are incorporated herein by reference intheir entirety.

This application is also related to U.S. patent application Ser. No.14/014,991 titled “Multi-Band Color Vision Filters and Method byLP-Optimization” filed Aug. 30, 2013 and to PCT/US2012/027790 titled“Multi-Band Color Vision Filters and Method by LP-Optimization” filedMar. 5, 2012, both of which are incorporated herein by reference intheir entirety.

FIELD OF THE INVENTION

The invention generally relates to optical filters that provideregulation and/or enhancement of chromatic and luminous aspects of thecolor appearance of light as seen by human color vision, generally toapplications of such optical filters, to applications of such opticalfilters in ophthalmic lenses, to therapeutic applications of suchoptical filters, to industrial and safety applications of such opticalfilters when incorporated, for example, in radiation-protective eyewear,to methods of designing such optical filters, to methods ofmanufacturing such optical filters, and to designs and methods ofincorporating such optical filters into optical systems including, forexample, eyewear, contact lenses, windows, coatings, and illuminants.

BACKGROUND

Optical filters are devices having wavelength-selective transmissionacting on sources or receivers of light. Such filters may be configuredto transform aspects of color appearance as seen by the human eye.Optical filters that improve or modify aspects of color vision mayprovide therapeutic benefit to persons with color vision deficiency, topersons with low-vision disorders and to persons with normal colorvision. Optical filters may provide eye-protection from high-energyradiation in the ultra-violet, visible, and/or infrared spectra.Apparatus incorporating optical filters affecting color vision and/orcolor appearance include eyewear, contact lenses, scope assemblies,cameras, windows, coatings and lamp assemblies. Such apparatus may begenerally referred to as optical systems. Apparatus wherein the opticalfilters act to modify light received by the eye using a lens or shielddisposed in front of the face or eye are generally referred to asophthalmic systems.

SUMMARY

Disclosed herein are methods for designing optical filters that, forexample, provide enhancement and/or regulation to the appearance ofcolor with respect to human color perception. The optical filter designsproduced by the described methods may be used as the basis formanufacturing specifications to fabricate the optical filters usingabsorptive optical materials, such as narrow-band absorbing dyes and/orbroad-band absorbing dyes. Such filters may be manufactured as a coatingapplied onto the surface of an optical substrate where the opticalsubstrate is substantially transparent, or may be incorporated into thebulk mass of an optical substrate, or both. The optical substrate may,for example, be incorporated into eyewear (e.g., eyeglasses, sunglasses,face-shields, monocles, safety lenses, contact lenses, or any othersuitable ophthalmic lenses), or may be incorporated into scopeassemblies (e.g. binoculars), or into camera lenses (e.g. as a filterplaced on a camera lens assembly), or may be incorporated into lampassemblies (e.g., light bulbs, flashlights), or may be incorporated intocoatings applied to a reflective surface (e.g. clear-coating appliedonto a paper or other substrate that has been pigmented by paint or by aprinting process).

An ophthalmic lens is a lens for use with an eye. An ophthalmic lens mayprovide optical (focusing) correction to the eye, or it may be of zeropower and provide no such correction. Eyeglass lenses (e.g., clear orsubstantially transparent lenses), tinted or colored lenses, sunglasslenses, polarized lenses, gradient lenses, photochromic lenses,multi-focal (e.g. progressive, bifocal and trifocal) lenses and contactlenses are examples of ophthalmic lenses.

Optical filters may be characterized by measurable properties pertainingto their transmittance spectra. Herein, the unqualified use of the term“filter” shall be understood to mean “optical filter”, unless otherwisespecified. Transmittance is the fraction of light that passes throughthe filter at a particular wavelength. The transmittance may be statedas a ratio, e.g. 0.40, or as a percent, e.g. 40%. The visiblewavelengths of light are between about 390 nanometers and about 750nanometers, however it is also reasonable to consider only wavelengthsbetween 400 nanometers and about 700 nanometers, or between 420nanometers and about 670 nanometers, because the human eye is relativelyinsensitive to light having a wavelength near the ends of the visiblespectrum and the properties of filters near the end of the visiblespectrum may therefore have little to no impact on color perception. Thetransmittance spectrum of a filter refers to its transmission across thevisible spectrum of light, unless otherwise specified herein. Thetransmittance spectra of filters may be simulated on a computer bytabulating the transmittance per wavelength, using a wavelength stepsize of 1 nanometer, for example, or using any other reasonable stepsize or other sampling method.

The mean transmittance of a filter is the average transmittance over acontiguous range of wavelengths, for example, the mean transmittancebetween 500 nanometers and 599 nanometers may be calculated by summingthe transmittance at each wavelength within the range using a step sizeof 1 nanometer, and then dividing the sum by 100.

The luminous transmittance of a filter is the weighted averagetransmittance of a standard illuminant by the filter, where theweighting function is a photopic luminous efficiency function defined bya standard observer model. In the present disclosure the luminoustransmittance of a filter is defined as the weighted averagetransmittance of CIE Standard Illuminant D65 and the weighting functionis the photopic luminous efficiency function defined by the CIE 19322-degree Standard Observer.

The white-point of a filter is the (x,y) chromaticity coordinates ofaverage daylight as seen through the filter, where average daylight isdefined as CIE Standard Illuminant D65 and the (x,y) chromaticitycoordinates are calculated according to the CIE 1932 2-degree StandardObserver and the CIE Yxy color space, unless otherwise specified.

The correlated color temperature of a filter is the temperaturecorresponding to a point on the black-body locus nearest to thewhite-point of the filter.

Measurement of the transmittance spectra of filters integrated into anophthalmic system may be performed for example by averaging themeasurement over a region of the lens corresponding to at least a10-degree field of view, when the ophthalmic system is used to filterlight received by the eye in a typical fashion. For example, thespectral measurement may be performed by passing a reference lightthrough an area on an eyeglass lens having a diameter between about 5millimeters and about 20 millimeters at the center of the lens, and thenperforming a spectral analysis on the light transformed by theophthalmic system. A similar measurement on a contact lens would use asmaller area that is appropriately chosen and proportional to thediameter of the lens. Measurement of the transmittance spectra offilters integrated into a lamp assembly may comprise averaging thespectral response of the system over a portion of the output beam, forexample corresponding to about 10% of the total output light power. Anyreasonable method of measuring the spectral response of a filterintegrated into a system may be used, wherein the method of measurementis appropriately chosen for consideration of the visual effect that thefilter causes (i.e. the effect as seen by a normal unaided human eye).

If an optical filter is incorporated into an ophthalmic lens, then itsproperties may be measured according to industry-standard conventionsand definitions, for example, the calculations just described aredefined with respect to eyewear by American National Standards InstituteZ80.3-2010 section 4.6 (transmittance), section 4.6.1 (luminoustransmittance), section 4.6.2 (mean transmittance), and section 4.6.3.1(white-point/chromaticity coordinates of average daylight). Similarcalculations for contact lenses are defined by ANSI Z80.20-2010, forintraocular lenses by ANSI Z80.7-2002, and for ski and snow goggles byASTM F659-12.

In one aspect, a computer implemented method for designing an opticalfilter for affecting color vision in a desired manner, where the filtercomprises a combination of two or more dye components, comprises using acomputer to simulate the state of a filter given in terms of itscomponent dye concentrations, which are given using a dye-formula in theform

F=α ₁Ω₁+ . . . α_(N)Ω_(N)

wherein, in the above formula, Ω_(i) represents the dye optical densityspectrum and a, represents the corresponding dye concentration for thei^(th) dye. And, in this method, the transmittance spectrum of thefilter, τ_(F), is simulated by the combination of the dye componentsaccording to the Beer-Lambert law,

τ_(F)=10^((−1×F))

and, the method comprises repeatedly (iteratively) executing a routinethat selects an optimal change to the dye formula (referred to herein asa dye increment), until the filter reaches a desired target luminoustransmittance (τ_(v)). And, at each repetition of the routine theoptimal change to the dye formula is selected from a collection ofcandidate changes, wherein each change corresponds to a small discreteincrement in dye concentration for a dye, and the optimal change is theone that maximizes the ratio of change in colorimetric performance perthe decrease in luminous transmittance of the corresponding candidatefilter, and/or the optimal change is the one that maximizes the ratio ofthe decrease in distance to the target white-point per the decrease inluminous transmittance of the candidate filter.

In some embodiments the target white-point is a single point in achromaticity space. In some embodiments the target white-point is acircular region in a chromaticity space. In some embodiments the targetwhite-point is a quadrilateral region in a chromaticity space. In someembodiments the target white-point is on the black-body locus at alocation corresponding to a black-body radiator with a color temperaturebetween about 2700 Kelvin and about 10000 Kelvin.

In some embodiments the target white-point is configured so that theresulting filter color is blue (i.e., that the apparent color of whitelight is transformed to a blue color when passing through the filter).In some embodiments the target white-point is configured so that thefilter color is violet. In some embodiments the target white-point isconfigured so that the filter color is pink. In some embodiments thetarget white-point is configured so that the filter color is purple. Insome embodiments the target white-point is configured so that the filtercolor is vermillion (vermillion is a pinkish-gray color). In someembodiments the target white-point is configured so that the filtercolor is yellow. In some embodiments the target white-point isconfigured so that the filter color is brown. In some embodiments thetarget white-point is configured so that the filter color is red. Insome embodiments the target white-point is configured so that the filtercolor is gray.

In some embodiments an additional constraint is provided to ensure thatthe transmittance of the filter between 580 nanometers and 600nanometers is at least 5%, or is at least 1/10^(th) of the luminoustransmittance, or is at least ⅕^(th) of the luminous transmittance ofthe filter.

In some embodiments, the method is modified to limit the maximumconcentration of certain dyes to comply with solubility limits necessaryfor manufacturing an article containing that dye in a desired polymericsubstrate.

In some embodiments, the method is modified to use recursive look-ahead,so that the calculation of the optimal change considers the bestincremental increase in dye concentration taking into account theanticipated future changes that may be needed to maintain the inputconstraint conditions.

In some embodiments, the method is configured to operate using a set ofstandard dyes, where a standard dye is defined as a dye having afull-width-half-maximum width greater than 40 nanometers around its peakabsorption wavelength. The peak absorption wavelength is the wavelengthwithin the visible spectrum where the optical density of the dye reachesits maximum. Some dyes may have higher optical density in regionsoutside the visible spectrum (e.g. in the ultra-violet or infraredspectrum), however these properties are not relevant to the design offilters for affecting color vision in a desired manner.

In some embodiments, the method is configured to operate using a set ofnarrow-band dyes, where a narrow-band dye is defined as a dye having afull-width-half-maximum width of at most 40 nanometers around its peakabsorption wavelength.

In some embodiments, the method is configured to operate using a set ofdyes including at least one narrow-band dye and at least one standarddye.

In some embodiments, the method is configured to use the red-greenseparation factor as the colorimetric performance measure.

In some embodiments, the colorimetric performance measure is calculatedby measuring the chromaticity gamut area of a set of reference colors(e.g. for a set of Munsell color swatches) as seen through the filter.

In another aspect, a colorimetric performance metric for characterizinga filter for affecting color vision comprises calculating the meantransmittance over three adjacent non-overlapping spectral regions: overa green region between about 500 nanometers and about 555 nanometers(τ_(G)), over a yellow region between about 555 nanometers and about 600nanometers (τ_(Y)), and over a red region between about 600 nanometersand about 650 nanometers (τ_(R)), and then calculating the luminoustransmittance of the filter (τ_(v)), and then calculating the red-greenseparation factor of the filter (Ψ_(RG)) using the formula:

Ψ_(RG)=((τ_(v)×((((τ_(G)+τ_(R))/2)/τ_(Y))−1))/(1−τ_(v))+1)

The red-green separation factor, as defined herein, is zero for neutralfilters (filters having a constant transmittance per wavelength), and isgreater than zero for filters that enhance the saturation and/orbrightness of colors organized along the red-green axis of color space.

In another aspect, a filter for affecting color vision in a desiredmanner comprises one or more narrow-band dyes, and the filter has aluminous transmittance of at least 40% and a red-green separation factorof at least 1.0.

In some embodiments, the filter comprises two or more narrow-band dyes.

In some embodiments, the filter comprises three or more narrow-banddyes.

In some embodiments, the filter comprises four or more narrow-band dyes.

In some embodiments, the filter comprises five or more narrow-band dyes.

In some embodiments, the filter comprises one or more narrow-band dyesand one or more standard dyes.

In some embodiments, the filter comprises two or more narrow-band dyesand one or more standard dyes.

In some embodiments, the filter comprises three or more narrow-band dyesand one or more standard dyes.

In some embodiments, the filter comprises four or more narrow-band dyesand one or more standard dyes.

In some embodiments, the filter comprises five or more narrow-band dyesand one or more standard dyes.

In some embodiments, the filter has a luminous transmittance that isgreater than 40% and has a red-green separation factor that is greaterthan 1.0.

In some embodiments, the filter has a luminous transmittance that isgreater than 40% and has a red-green separation factor that is greaterthan 1.25.

In some embodiments, the filter has a luminous transmittance that isgreater than 40% and has a red-green separation factor that is greaterthan 1.5.

In some embodiments, the filter has a luminous transmittance that isgreater than 40% and has a red-green separation factor that is greaterthan 2.0.

In some embodiments, the filter has a luminous transmittance that isgreater than 50% and has a red-green separation factor that is greaterthan 1.0.

In some embodiments, the filter has a luminous transmittance that isgreater than 50% and has a red-green separation factor that is greaterthan 1.25.

In some embodiments, the filter has a luminous transmittance that isgreater than 50% and has a red-green separation factor that is greaterthan 1.5.

In some embodiments, the filter has a luminous transmittance that isgreater than 50% and has a red-green separation factor that is greaterthan 2.0.

In some embodiments, the filter has a luminous transmittance that isgreater than 60% and has a red-green separation factor that is greaterthan 1.0.

In some embodiments, the filter has a luminous transmittance that isgreater than 60% and has a red-green separation factor that is greaterthan 1.25.

In some embodiments, the filter has a luminous transmittance that isgreater than 60% and has a red-green separation factor that is greaterthan 1.5.

In some embodiments, the filter has a luminous transmittance that isgreater than 60% and has a red-green separation factor that is greaterthan 2.0.

In some embodiments, wherein the filter has a luminous transmittance ofat least about 40% and the filter has a red-green separation factor ofat least 1.0, the filter color is blue.

In some embodiments, wherein the filter has a luminous transmittance ofat least about 40% and the filter has a red-green separation factor ofat least 1.0, the filter color is blue-green.

In some embodiments, wherein the filter has a luminous transmittance ofat least about 40% and the filter has a red-green separation factor ofat least 1.0, the filter color is violet.

In some embodiments, wherein the filter has a luminous transmittance ofat least about 40% and the filter has a red-green separation factor ofat least 1.0, the filter color is purple.

In some embodiments, wherein the filter has a luminous transmittance ofat least about 40% and the filter has a red-green separation factor ofat least 1.0, the filter color is pink.

In some embodiments, wherein the filter has a luminous transmittance ofat least about 40% and the filter has a red-green separation factor ofat least 1.0, the filter color is vermillion (vermillion is apinkish-gray).

In some embodiments, the white-point of the filter is configured to havea correlated color temperature between 2700 Kelvin and 10000 Kelvin andthe distance of the filter white-point to the black-body locus is atmost about 0.05 units in the CIE (x,y) 1932 2-degree standard observerchromaticity space.

In some embodiments, the white-point of the filter is configured to havea correlated color temperature between 2700 Kelvin and 10000 Kelvin andthe distance of the filter white-point to the black-body locus is atmost about 0.025 units in the CIE (x,y) 1932 2-degree standard observerchromaticity space.

In some embodiments, the filter comprises a first narrow-band dye withpeak absorption wavelength of about 575 nanometers, and a secondnarrow-band dye with peak absorption wavelength of about 595 nanometers.

In some embodiments, the filter comprises a first narrow-band dye withpeak absorption wavelength of about 575 nanometers, and a secondnarrow-band dye with peak absorption wavelength of about 595 nanometers,and the concentration of the dyes are configured so that thetransmittance of the filter at 575 nanometers is about 10%+/−5%.

In some embodiments, the filter comprises a first narrow-band dye withpeak absorption wavelength of about 575 nanometers, and a secondnarrow-band dye with peak absorption wavelength of about 595 nanometers,and the concentration of the dyes are configured so that thetransmittance of the filter at 595 nanometers is about 5%+/−3%.

In some embodiments, the filter comprises a first narrow-band dye withpeak absorption wavelength of about 595 nanometers, and a secondnarrow-band dye with peak absorption wavelength of about 475 nanometers,and the dye concentrations are configured so that the transmittance ofthe filter at 475 nanometers is at least about 4 times greater than thetransmittance of the filter at 595 nanometers, and so that the luminoustransmittance of the filter is at least 40%, or is at least 50%, or isat least 60%.

In some embodiments, the filter comprises a first narrow-band dye withpeak absorption wavelength of about 575 nanometers, and a secondnarrow-band dye with peak absorption wavelength of about 475 nanometers,and the dye concentrations are configured so that the transmittance ofthe filter at 475 nanometers is at least about 3 times greater than thetransmittance of the filter at 575 nanometers, and so that the luminoustransmittance of the filter is at least 40%, or is at least 50%, or isat least 60%.

In another aspect, a method for prescribing an ophthalmic lens to anindividual suffering from color vision deficiency comprises testing thecolor vision of the individual and then prescribing (recommending orselecting) a lens containing an optical filter wherein if the individualhas deuteranomaly then a lens is selected such that the transmittance ofthe filter at 575 nanometers is at least two times greater than thetransmittance at 595 nanometers, and/or if the individual hasprotanomaly then a lens is selected such that the transmittance of thefilter at 595 nanometers is at least two times greater than thetransmittance at 575 nanometers.

In another aspect, a method for prescribing an ophthalmic contact lensto an individual suffering from color vision deficiency comprisestesting the color vision of the individual and then prescribing(recommending or selecting) a lens containing an optical filter whereinif the individual has deuteranomaly then a lens is selected such thatthe transmittance of the filter at 575 nanometers is at least two timesgreater than the transmittance at 595 nanometers, and/or if theindividual has protanomaly then a lens is selected such that thetransmittance of the filter at 595 nanometers is at least two timesgreater than the transmittance at 575 nanometers, and the luminoustransmittance of the filter is greater than about 70%.

In another aspect, a filter for affecting color vision in a desiredmanner comprises one or more narrow-band dyes, and the filter has aluminous transmittance of at least about 70%, and has a meantransmittance between 390 nanometers and 430 nanometers of at most 25%,and the filter comprises a narrow-band dye having a peak absorptionwavelength of about 595 nanometers, and the concentration of thenarrow-band dye is configured so that the transmittance of the filter at595 nanometers is at most about 75%.

In some embodiments, the filter has a luminous transmittance of about85% and has a mean transmittance between 390 nanometers and 430nanometers of about 20%.

In some embodiments, the filter has a luminous transmittance of about75% and has a mean transmittance between 390 nanometers and 430nanometers of about 5%.

In some embodiments, the filter comprises a first narrow-band absorbingdye having a peak absorption wavelength of about 595 nanometers, and asecond narrow-band dye having a peak absorption wavelength of about 405nanometers, and the second narrow-band dye also has a lesser absorptionpeak at about 510 nanometers.

In some embodiments, the filter comprises a first narrow-band absorbingdye having a peak absorption wavelength of about 595 nanometers, and asecond narrow-band dye having a peak absorption wavelength of about 420nanometers, and the second narrow-band dye also has a lesser absorptionpeak at about 525 nanometers.

In another aspect, a filter for affecting color vision in a desiredmanner comprises one or more narrow-band dyes and one or moreblue-absorbing standard dyes, and the filter has a luminoustransmittance of at most 40%, and the filter transmittance between 390nanometers and 425 nanometers is at most 1%.

In some embodiments, the filter transmittance between 390 nanometers and450 nanometers is at most 1%.

In some embodiments, the filter comprises a narrow-band dye with a peakabsorption wavelength of about 595 nanometers, and the concentration ofsaid narrow-band dye is configured so that the transmittance of thefilter at 595 nanometers is at most about 10%.

In another aspect, a filter comprising one or more narrow-band dyes andoptionally one or more standard dyes, where the filter is configured toaffect color vision in a desired manner, is incorporated into anophthalmic system.

In some embodiments, the ophthalmic system is a type of eyewearcomprising an ophthalmic lens and/or window, for example a spectaclelens, sunglass lens or face shield. In some such embodiments the filtermay be incorporated so that a portion of the visual field is affectedwhere the portion of the visual field is where near-field viewingconditions occur. In some such embodiments the filter may beincorporated so that a portion of the visual field is affected where theportion of the visual field is where far-field viewing conditions occur.

In some embodiments wherein the ophthalmic system is a type of eyewear,the filter is incorporated into a coating that is applied to the surfaceof a lens substrate.

In some embodiments wherein the ophthalmic system is a type of eyewear,the filter is incorporated into the bulk material of a lens substrate.

In some embodiments wherein the ophthalmic system is a type of eyewear,the filter is incorporated into both the bulk material of a lenssubstrate and into a coating that is applied to the surface of the lenssubstrate.

In some embodiments wherein the ophthalmic system is a type of eyewear,the lens assembly includes a second filter where the second filter is orcomprises a photochromic dye, or is or comprises a linear polarizer, oris or comprises a circular polarizer.

In some embodiments the ophthalmic system comprises a contact lens.

In some embodiments the ophthalmic system comprises an intra-ocularlens.

In another aspect, a filter affecting color vision in a desired manner,where the filter comprises one or more narrow-band dyes, is incorporatedinto an optical system.

In some embodiments, the optical system is a lamp assembly and thefilter is incorporated so that some or all of the light emitted by thelamp is filtered.

In some embodiments, the lamp assembly is a flashlight, headlight orsimilar portable light source.

In some embodiments, the optical system is light bulb, light fixture orsimilar permanently-installable light source.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: Process flow diagram depicting iterative method of designing anoptimized dye-formula for a filter affecting color vision in a desiredmanner.

FIG. 2: Process flow diagram depicting method of measuring candidateimprovements to a dye-formula for a filter affecting color vision in adesired manner.

FIG. 3: Process flow diagram depicting method of measuring improvementfor a candidate improved filter where the improvement desired is toincrease a colorimetric performance metric.

FIG. 4: Process flow diagram depicting method of measuring improvementfor a candidate improved filter where the improvement desired is torestore compliance with a target white-point constraint.

FIG. 5: Absorptance spectra of the S-cone, M-cone, L-cone and rodphotopigments for a typical human eye.

FIG. 6: Chromaticity diagram showing regions having canonical colornames, and a triangular region comprising intermediate colors betweengreen and red.

FIG. 7: Graph of the distance between the white-point and the spectrallocus per wavelength, and a rectangular region denoting the wavelengthscorresponding to spectral colors between green and red.

FIG. 8: Optical density spectra of selected standard dyes.

FIG. 9: Transmittance spectra of blue-colored filters comprisingstandard yellow-absorbing dyes.

FIG. 10: Transmittance spectra of pink-colored filters comprisingstandard yellow-absorbing dyes.

FIG. 11: Transmittance spectra of blue-colored filters comprisingneodymium-oxide.

FIG. 12: Optical density spectra of a standard yellow-absorbing dye, andof a narrow-band yellow-absorbing dye.

FIG. 13: Optical density spectra of selected narrow-band dyes.

FIG. 14: Transmittance spectra of blue-colored filters comprising asingle narrow-band dye.

FIG. 15: Transmittance spectra of pink-colored filters comprising asingle narrow-band dye.

FIG. 16: Transmittance spectra of blue-colored filters comprising aplurality of narrow-band dyes.

FIG. 17: Transmittance spectra of vermillion-colored filters comprisinga plurality of narrow-band dyes.

FIG. 18: Transmittance spectra of gray-colored filters comprising aplurality of narrow-band dyes.

FIG. 19: Transmittance spectra of HEV (high energy visible)radiation-absorbing filters comprising a plurality of narrow-band dyesand/or standard dyes.

FIG. 20: Transmittance spectra of achromatopsia-assistive filterscomprising a plurality of narrow-band dyes and/or standard dyes.

FIG. 21: Chromaticity plot showing white-point locations of selectedfilters, and chromaticity regions for categorization of filter colors.

FIG. 22: Scatter plot of luminous transmittance versus red-greenseparation factor for selected filter examples, and three regions forcategorization of colorimetric filter performance.

FIG. 23A: Schematic diagram showing construction of an ophthalmic lenscomprising a functional dye-based filter applied as a bonded coating ona lens substrate.

FIG. 23B: Schematic diagram of a lamp source assembly comprising afunctional dye-based filter incorporated as an optical windowintersecting with the lamp output beam.

FIG. 24A: Diagram showing region on a lens where a filter can be appliedto provide a desired effect on color vision for near-field viewingconditions.

FIG. 24B: Diagram showing region on a lens where a filter can be appliedto provide a desired effect on color vision for far-field viewingconditions.

FIG. 25: Example process flow diagram for describing and demonstratingthe syntax and structure of process flow diagrams as they appear inother figures.

FIG. 26: Table of normalized optical density spectra of standard dyes.

FIG. 27: Table of transmittance spectra for DCB series of opticalfilters.

FIG. 28: Table of transmittance spectra for DCP series of opticalfilters.

FIG. 29: Table of transmittance spectra for ACE series of opticalfilters.

FIG. 30: Table of normalized optical density spectra of narrow-banddyes.

FIG. 31: Table of transmittance spectra for DMB series of opticalfilters.

FIG. 32: Table of transmittance spectra for DMP series of opticalfilters.

FIG. 33: Table of transmittance spectra for CXB series of opticalfilters.

FIG. 34: Table of transmittance spectra for CXV series of opticalfilters.

FIG. 35: Table of transmittance spectra for CXN series of opticalfilters.

FIG. 36: Table of transmittance spectra for UVH series of opticalfilters.

FIG. 37: Table of transmittance spectra for ACR series of opticalfilters.

FIG. 38: Table of properties of filters having Ψ_(RG)>1 and τ_(v)>0.40.

FIG. 39: Table of properties of filters having Ψ_(RG)<1.

DETAILED DESCRIPTION

The following detailed description should be read with reference to thedrawings, in which identical reference numbers refer to like elementsthroughout the different figures. The drawings, which are notnecessarily to scale, depict selective embodiments and are not intendedto limit the scope of the invention. The detailed descriptionillustrates by way of example, not by way of limitation, the principlesof the invention. This description will clearly enable one skilled inthe art to make and use the invention, and describes severalembodiments, adaptations, variations, alternatives and uses of theinvention, including what is presently believed to be the best mode ofcarrying out the invention. As used in this specification and theappended claims, the singular forms “a,” “an,” and “the” include pluralreferents unless the context clearly indicates otherwise.

Optical filters may be incorporated into eyewear to provide a variety ofuseful effects for assisting with color vision, in particular forproviding better color vision to persons with color vision deficiency.As described in U.S. patent application Ser. No. 14/014,991, therelevant design constraints for optical filters affecting color visionin a desired manner are readily stated in the form of a linear programand rapidly solvable with a unique global optimum solution given a costfunction. Such constraints include, for example, the chromaticity and/orluminosity bounds required on the appearance of any specified lightsource as seen through the filter. The constraints of a well-formed(solvable) linear program form a n-dimensional polyhedron where n is thenumber of basis elements. The basis elements are, for example,monochromatic light sources (discrete dirac-delta functions) for eachwavelength of light, or may be Gaussian basis functions, or any functionof transmittance versus wavelength. Furthermore, a general property ofsolutions to linear programs is that they are necessarily located at thevertex of the n-dimensional constraining polyhedron. This type ofoptimality condition is equivalent to the statement that it is alwayspreferable to maximize utilization of a particular basis element (e.g.an element with the least cost), prior to any utilization of a basiselement with higher cost. In the absence of any specified constraints onthe minimum and maximum spectral transmittance, the optimal filter musthave a binary transmittance function per wavelength, meaning that ateach wavelength the filter is either 100% transmitting or 100% blocking.In other words, any filter solution that has smoothly changingtransmittance function versus wavelength corresponds to linear programsolution that is located on the interior of the constraint polyhedron,and therefore is not optimal since it does not minimize cost (or,equivalently, maximize benefit) with respect to the constrainingconditions. In the event where constraints are specified, for examplegoverning the minimum necessary luminosity for certain lights, these canlead to regions where the minimum spectral transmittance has a lowerbound. For example, the use of such lower bound constraints can resultin the appearance of a shoulder feature that extends from a pass-bandinto an adjacent stop-band. In summary, optimized filters for affectingcolor vision in a desired manner are those with one or more stop-band(notch) cutouts, and where the absolute magnitude of the slope at eachband transition is as high as possible. This characteristic of the bandtransitions of such filters may also be described as being “sharp”,“narrow-band width”, “high-frequency”, “high attenuation factor” orsimilar terms.

Means for implementing filters with one or more sharp stop-bands asdescribed include dielectric stacks (equivalent to an optical infiniteimpulse response filter), polarization retarder stacks (equivalent to anoptical finite impulse response filter), absorptive dyes, fluorescentdyes, and hybrid approaches comprising two or more of the aforementionedmeans. Dielectric stacks and polarization retarder stacks can both beconsidered types of general filter design technologies, in that they arecapable of being adapted to nearly arbitrary target filterspecifications. Such technologies are appropriate for use with thedesign method based on linear programming described above. However, forthe design of filters based on combinations of dyes, it may bepreferable to use a different method that is preferable for determiningthe appropriate dye-formula using an iterative algorithm thataccommodates the non-linear mixing properties of dyes. The properties ofdyes are inherently non-linear (being characterized according to theBeer-Lambert law), and therefore are not suitable as inputs to a linearprogram solver. In addition, design of dye-based filters posesadditional problems including: 1) dyes are limited to discrete choicesdue to underlying chemistry, and the optical density spectrum of dyesavailable for formulation may not be readily modified. 2) the spectralabsorptance of dyes, e.g. in a polymeric carrier matrix, are not ideallyselective and often have side-bands or otherwise cause absorption indisparate areas of the spectrum, 3) dyes impart coloration to filterswhich may have aesthetic consequences (in particular when incorporatedinto eyewear). Given a theoretically optimal target transmittancespectrum (e.g. as calculated by the method of linear programming), itmay be difficult to find a combination of dyes that approximates thetarget accurately while also providing adequate performance with respectto the desired effect on color vision. In addition, for filters thatcomprise a complex formula of two or more dye components, the filterproperties change under any scalar modification of the formula. Forexample, suppose a dye formula is diluted in equal proportion over itsdye components to arrive at a new filter with a higher luminoustransmittance. The diluted filter will be less optimal than a filterthat is designed (e.g. using the method described below) to have thesame target luminous transmittance as the diluted filter.

An iterative method for designing and optimizing filters that affectcolor vision in a desired manner, where the filters are based oncombinations of dyes (specified using a dye-formula), is described indetail below. This method, when implemented on a computer, enablesautomatic optimization of a dye-formula for filter affecting colorvision in a desired manner. The dye-formulas provided by this method canbe used as the basis for a manufacturing specification of such filters.Examples of filters designed using this method and/or variations of themethod, the filters' desired effects on color vision, and other detaileddescriptions are provided along with description of FIGS. 14-20. Themethod, as described herein, is capable of producing dye-formulas forfilters that are optimized with respect to a colorimetric performancemetric, while also satisfying one or more constraints, e.g. constraintson the chromaticity and/or luminosity of certain specified lightsources. In some variants of the method the colorimetric performancemetric is defined as the red-green separation factor, which is definedand described in detail below. In some variants the colorimetricperformance metric is the chromaticity gamut area of a set of specifiedreference colors. In some variants the colorimetric performance metricis the minimization of transmission of high-energy visible light (i.e.short-wavelength blue light). In some variants the colorimetricconstraints pertain to the luminosity and/or chromaticity of a specifiedwhite light, for example, by requiring that the Standard Illuminant D65has a particular luminosity and its chromaticity (as viewed through thefilter) is bounded within a particular region in chromaticity space. Insome variants the colorimetric constraints pertain to the luminosity ofa specified yellow light, for example by requiring that yellow LEDs havea minimum luminosity necessary to enable visibility of such lights whenviewed through the filter. In some variants the colorimetric constraintspertain to the limitation of scotopic transmittance to be a fraction ofthe luminous transmittance, for example less than about one third(scotopic light is light that is received by the rod cell photopigmentcomprising wavelengths between about 430 nanometers and about 570nanometers).

FIG. 1 is a process flow diagram depicting an embodiment of theaforementioned iterative method (algorithm) of optimizing a dye-formulafor a filter given a specification of design criteria. The designcriteria shown include a vector of the initial dye concentrations 101,the optical density spectra of dyes available for formulation (componentdyes) 102, the target white-point of the filter 103 (e.g. the desiredCIE 1932 (x,y) chromaticity coordinates of a reference illuminant), andthe power spectrum of the reference illuminant 104. Typically thereference illuminant is CIE Standard Illuminant D65, but may also beanother illuminant such as that of a different phase of daylight, or afluorescent lamp, or of a light-emitting diode, or any other specifiedlight source. The design criteria are provided as inputs to the dyeformula optimization algorithm 105, within which an iterated processtakes place, wherein an initial set of dye concentrations is iterativelyupdated until the process is terminated, and the state of the dyeconcentrations upon termination is a set of optimized dye concentrations112.

The iteration process is initialized by simulating a filter using theinitial dye concentrations and the component dye optical densityspectra. Typically the initial dye concentrations are all zero, i.e. theinitially simulated filter is fully transparent. The simulated filter isthen checked with respect to the specified white-point constraints. Thewhite-point of the filter is calculated in terms of a two-dimensionalchromaticity coordinate in a suitable color space, for example CIE Yxyor CIE LUV color space. The white-point constraint check comprisesmeasuring the distance between the target white-point 103 and thewhite-point provided by the currently simulated filter with respect tothe reference illuminant. If the target white-point is a single point,then the distance is a vector length. If the target white-point is a2-dimensional region, then the distance is the length of the shortestline connecting the currently provided white-point to the boundary ofthe region, or zero for points located on the boundary of the region orlocated within the region. The filter white-point check is considered topass (i.e., is in compliance) if the distance value is less than anappropriately chosen epsilon, for example about 0.001 units in the CIE(x,y) chromaticity space. In some variations a larger epsilon value(e.g. 0.05 units in the CIE (x,y) chromaticity space) may be chosen,where the use of a larger epsilon value is equivalent to defining acircular, curved or rounded target white-point region. If the filterwhite-point check is considered to pass, then a sub-process is performedwherein improvements to the colorimetric performance of the filter areconsidered 108. If the check is considered to not pass (i.e. is not incompliance), then a sub-process is performed wherein improvements to thefilter white-point compliance are considered 107. The two aforementionedsub-processes 107 108 analyze the current dye-formula and then select anew dye-formula that corresponds to a new simulated filter. These dataare then provided to another sub-process where the luminoustransmittance of the filter is measured 110. If the luminoustransmittance is less than or equal to the target luminosity 109, thenthe dye-formula optimization process is terminated and the current dyeconcentrations are output as the final optimized dye-formula 112. If theluminous transmittance is greater than the target luminosity, then thedye concentration vector 111 is updated and the process flow as justdescribed is repeated by returning to the filter white-point check stepindicated at 106.

Each time the process loop shown is executed, the concentration of oneof the dyes is increased, causing a non-linear transformation to thecurrently simulated filter. As the concentrations are monotonicallyincreasing with each iteration, the luminosity of the filter will belesser with each iteration, eventually resulting in the termination ofthe process when the filter reaches the desired target luminosity. Ineach iteration, the amount of change in dye concentration amounts to asmall discrete step, which, over time approximate a continuous line inan n-dimensional space where n is the number of dye optical densityspectra 102 provided from the set of dyes available for formulation. Theoptimality of the resulting filter is a consequence of the optimality ofthe each step along this line. The method of choosing the optimal stepin each of the sub-processes 106 and 107 is described in further detailbelow.

The sub-processes 106 and 107 in FIG. 1 both consider possibleimprovements to a dye-formula, and utilize a common algorithmicstructure for simulating the possible improvements, then measuring theefficacy of the candidate improved filters, and then selecting the bestimprovement available from the candidate options. A description of thisgeneral process is depicted in FIG. 2. The sub-processes 106 and 107correspond to two variations of this general process, where differenttypes of improvements are considered. The calculation of efficacy forthe different types of improvements are explained below along withdescriptions of FIG. 3 and FIG. 4.

Referring now to FIG. 2, the method of selecting the optimal improvementto a dye-formula given a set of candidate improvements, is depicted as aprocess flow diagram. Herein the process is initialized from the currentset of dye concentrations 201, the set of optical density spectra ofdyes available for formulation 202, and the current simulated filtercorresponding to the mixture of the component dyes in theircorresponding concentrations according to the dye formula 204, thetransmittance spectrum of the current filter 206, and a set of dyeconcentration increments 203 consisting of a dye increment correspondingto each dye. The dye concentration increments are a small amount bywhich the concentration of a corresponding dye will be increased. Forexample, by increasing the total concentration by about 0.001 units. Thesmall dye increment values, when considered over time, approximate acontinuous change in concentration for each dye. The increment size mustbe selected appropriately to produce a good approximation of continuity,otherwise the algorithm could result in a non-optimal solution. For eachdye concentration increment, a filter is simulated 205 corresponding tothe current dye-formula where the concentration of the corresponding dyehas been increased accordingly, resulting in a collection oftransmittance spectra of candidate filters 207. For each candidatefilter corresponding to a dye increment, the improvement efficacy withrespect to the dye increment is calculated 209, which involves acomparison between the candidate filter and the current filter 206. Thedye increment efficacy scores are then collected 210 and then sorted tochoose the dye increment with the best performance 211 resulting in anupdated and optimally improved filter 212, and a new set of dyeconcentrations corresponding to the improved filter 213, and theefficacy score corresponding to the dye increment that was chosen asoptimal 214. The new dye concentrations are then returned to theenclosing routine which is described above along with FIG. 1. Inaddition, the efficacy score 214 can be monitored at each step to obtaininsight into the amount of improvement being achieved as the enclosingiterative design method executes.

The calculation of a candidate improved filter 302 as compared to thecurrent filter 301, with respect to a colorimetric performance measure,is depicted in FIG. 3. The calculation is initialized by evaluating thecolorimetric performance for both the current filter 303 and for thecandidate filter 304, and by calculating the luminous transmittance ofthe current filter 305 and of the candidate filter 306. Then, the amountof change in both quantities is calculated, providing the amount ofchange in colorimetric performance between the current and candidatefilters 307, and the amount of decrease in luminosity between thecurrent and candidate filters 308. Note that the candidate filter alwayshas a lower luminous transmittance than the current filter, however thecolorimetric performance may be either greater or lesser depending onwhich dye concentration was incremented in the formulation of thecandidate filter. The two differences are then compared as a ratio 309giving the rate of change in colorimetric performance per change inluminous transmittance, which can be understood as a measure of theimprovement efficacy of the corresponding dye increment 310 with respectto the colorimetric performance.

In the above calculation it may be useful to understand that, given acurrent dye formula and corresponding filter, and the set of dyesavailable for formulation, it is desired to increase the concentrationof the dye that is most effective toward improving the colorimetricperformance, however the total amount of dye that can be “loaded” into aformula is limited by the target luminosity of the filter. Therefore,the dye that maximally increases the colorimetric performance may not bethe optimal dye to increase in concentration if it also has a high costin terms of how much it decreases the filter luminosity. If we consideravailable luminosity as a resource that is spent/cost that is incurredby increasing dye concentration, then the optimal dye to increase is theone that gives the best cost:benefit ratio between the luminosity andthe colorimetric performance. The calculation of FIG. 3 as describedabove can be understood as a calculation of that cost:benefit ratio.

In another variation of the method of designing optimal filters from adye concentration formula, the size of the dye increments can be variedfor each dye, so that at each step the change in luminosity is heldconstant for all filter candidates.

The selection of appropriate colorimetric performance measures foraffecting color vision in a desired manner is described in furtherdetail below along with examples of filters designed accordingly.

Another calculation concerning evaluation of candidate improvements to adye formula is depicted in FIG. 4, wherein the objective is to determinethe improvement efficacy with respect to restoring compliance of thecurrent filter with the target white-point constraint. In thiscalculation, the transmittance spectrum of the current filter 401 isevaluated to determine its distance to the target white-point 405, andits luminous transmittance 407. The candidate improved filter 402 isevaluated according to the same at 406 and 408. The distance to thetarget white-point is defined with respect to the target white-point404, which may be a chromaticity coordinate, or a region in chromaticityspace as described previously, and with respect to the referenceilluminant 403, also described previously. The target white-pointdistance and luminosity values are then compared in a differenceoperation at 409 and 410, respectively, and then input into a ratiocalculation at 411 to determine an overall measure of improvement forthe candidate filter with respect to the white-point constraintcriteria.

The basic properties of the calculation just described is similar tothat of FIG. 3, wherein the goal is to determine the cost:benefit ratioof the dye increment corresponding to the candidate filter. However inthe calculation depicted by FIG. 4, the dye with greatest efficacy isthe one that reduces the target white-point distance with the leastreduction in filter luminosity. In other words, it is desired to restorethe white-point to compliance without making the filter unnecessarilydark.

In another variation of the above calculation, the luminositycalculation at 407 and 408 is replaced with a colorimetric performancemeasure, as in FIG. 3 at 303 and 304. In this variation the filtercandidate with maximum efficacy is the one that restores white-pointcompliance with the least reduction in colorimetric performance.

The iterative method depicted in FIG. 1 can now be understood, togetherwith the details of the sub-processes defined by FIG. 2, FIG. 3 and FIG.4, as a detailed description of the method by which filters intended toaffect color vision in a desired manner can be designed as formulationsof dye concentrations from a set of available dyes.

In one variation of the iterative method, the iterations proceedsubstantially as described above, wherein at each step the processconsiders improvements to either the target white-point constraintcompliance or to the desired colorimetric performance. For sufficientlysmall dye increment values this method may be adequate, however in somecases a higher-order version of the iterative process may be preferred.In such a variant, the repetitions of the process are recursivelycalculated, in order to simulate the optimality of a filter candidateafter several steps according to different dye increment selections, andthen selecting the dye increment corresponding to the optimal choiceconsidering this larger set of candidates. The depth of recursivecalculation possible is limited by available computing resources (e.g.processor time and memory). In another variation the dye increments maybe considered that induce a change in more than one dye component, i.e.,the “step direction” is not limited to movements in only one axis of then-dimensional solution space.

Additional variations of the process, which are configured to result infilters that are preferable for certain applications, are described indetail along with additional figures below.

Filters that affect color vision in useful ways, when integrated into anoptical system, provide a spectral transmittance that modifies the powerspectrum of light passing through the system. Such filters, given asuitable means of manufacturing, may be incorporated into eyewear orinto contact lenses, for example, to transform the image received by theeye. Such filters may also be incorporated into lamp assemblies totransform the light used to illuminate a working area.

The nature of human color vision is based on the spectral sensitivity ofphotoreceptors in the eye, each of which respond broadly to a particularsub-band of light within the visible spectrum. The normalizedabsorptance of the photoreceptor pigments are shown in the graph of FIG.5, wherein the S-cone absorptance 501 has a peak absorptance at about440 nanometers, the M-cone absorptance 503 has a peak absorptance atabout 540 nanometers, the L-cone absorptance 504 has a peak absorptanceat about 565 nanometers, and the rod cell absorptance has a peakabsorptance 502 at about 510 nanometers. The perception of color inhumans is formed by comparing the relative stimulation of neighboringphotoreceptors of the three different types which are packed together ina mosaic of 6-7 million photoreceptor cells on the surface of theretina.

The space of all possible visible power spectra is an infinitedimensional vector space, which is projected onto a 3 dimensional spaceof perceived color and lightness. The projection is described as themathematical concept of a Hilbert space. Humans with normal color visionare able to distinguish approximately 1 million unique shades of color.Different spectral stimuli that induce the same color sensation arecalled metamers. Vision based on three distinct cone classes is calledtrichromatic color vision. The 3 dimensional space of apparent color canbe decomposed into three channels which are essentially orthogonalpercepts: that of lightness or brightness (spanning from white toblack), and two channels of chromaticity comprising the blue-yellowchannel (organizing color percepts by their blue-ness to yellow-ness)and the red-green channel (organizing color percepts by their red-nessto green-ness). The blue-yellow channel corresponds to the comparison ofthe S-cone stimulation versus the combined M-cone and L-conestimulation. The red-green channel corresponds to the comparison of theM-cone stimulation to that of the L-cone stimulation. Vision fromstimulation of the cone cells is referred to as photopic vision, andvision from stimulation of the rod cells is scotopic vision. Rod-cellphotoreceptors are overwhelmed (bleached) by bright light, and thusscotopic vision, which is a monochromatic visual mechanism, is onlyactive at night time and/or in very low-light conditions. Activitiessuch as driving a car at night are actually performed using photopicvision, due to the brightness of car headlights and traffic signallights.

It is observable from the graphs of photoreceptor absorptance in FIG. 5that there is substantial overlap between the absorptance curves, inparticular of the M-cone and L-cone. Furthermore, in the humanpopulation there are genetic variations causing the spectral position ofthe M-cone and L-cone to vary between individuals. Persons withincreased overlap between the M-cone and L-cone absorptance are calledred-green color blind, although it is more technically correct to referto this condition as color vision deficiency (CVD). CVD is classifiedaccording to type (either an anomaly of the M-cone (deuteranomaly) or ofthe L-cone (protanomaly)) and according to the extent (corresponding tothe amount of increased overlap, which can be mild, moderate, severe ortotal). For cases of CVD where the overlap is less than total,trichromatic vision is still functional, although may be significantlyimpaired. For a mild impairment the number of perceivable colors maydrop to 100 thousand (10% of normal), while for a strong individual itmay be as low as 10 thousand (1% of normal). Filters disclosed hereinare generally found to be useful for enhancement of trichromatic vision,including that of normal trichromatic vision, as well as for most casesof anomalous trichromatic vision. The fundamental mechanism of how thesefilters modify color vision is that they selectively block light withwavelengths corresponding to locations where significant amount ofoverlap between the photopigment absorptance curves is found. Inaddition to red-green color blindness, other types of anomaloustrichromatic vision include tritanomaly (a condition where S-conefunction is deficient), general loss of chromatic sensitivity (acondition often experienced with low-vision complications such asretinitis pigmentosa and glaucoma), and incomplete achromatopsia (acondition related to severe dysfunction or nearly total lack of conecells, but having functional rod cells, sometimes also called“day-blindness”).

For the purpose of designing filters that assist with red-green colorblindness, and in particular for filters that also have a high luminoustransmittance, a colorimetric performance metric is provided herein thatis easy to calculate. The metric is referred to herein as the red-greenseparation factor, which is also denoted Ψ_(RG) in this disclosure.Given the transmittance spectrum of a filter, τ(λ), the calculation ofred-green separation factor is given according to the formula:

Ψ_(RG)=((τ_(v)×((((τ_(G)+τ_(R))/2)/τ_(Y))−1))/(1−τ_(v))+1)

Wherein, in the above formula, τ_(v) is the luminous transmittance ofthe filter, τ_(G) is the average spectral transmittance of the filterbetween 500 nanometers and 550 nanometers, τ_(Y) is the average spectraltransmittance of the filter between 555 nanometers and 600 nanometers,τ_(R) is the average spectral transmittance of the filter between 600nanometers and 650 nanometers. The use of the red-green separationfactor as a colorimetric performance measure has been found by theinventors to be preferable for use with the disclosed iterative filterdesign method when the target luminosity of the filter is greater thanabout 40%. For target luminosity of less than 40%, other colorimetricperformance measures, such as the chromaticity gamut area of a set ofreference colors (as described in U.S. patent application Ser. No.14/014,991), may be preferable.

The chromaticity diagram shown in FIG. 6 includes a plurality of regionswhich are labeled using an alpha-numeric code according to theircanonical color name. Filters that have a high red-green separationfactor are characterized by a stop-band or general inhibition oftransmittance over wavelengths of light corresponding to spectral colorsconsidered to be between red (R) and green (G). Spectral colors are theapparent perceived color of a monochromatic light, which correspond tochromaticity coordinates located on the spectral locus in a chromaticitydiagram. A monochromatic light having a wavelength of about 580nanometers is considered yellow (Y), and at wavelengths between 555 to580 nanometers are considered (gY) greenish-yellow, (yG)yellowish-green, or (YG) yellow-green, and at wavelengths between 590 to610 nanometers is considered to be yellowish-orange (yO), orange (O)reddish-orange (rO). These regions taken together approximately span theintermediate colors between red and green, and a filter inhibiting thetransmission of these wavelengths will tend to amplify the apparentsaturation of red and green colors as typically observed in the man-madeand natural environment. The location on the chromaticity locus of thecolor of monochromatic light with wavelength 555 nanometers is indicatedat 601, and the location on the chromaticity locus of the color ofmonochromatic light with wavelength 600 nanometers is indicated at 602.The point on the chromaticity diagram corresponding to StandardIlluminant D65 is indicated at 603. The straight lines connecting 603 to601 and 603 to 602 define the distance from these monochromatic colorcoordinates to the specified white-point.

The plot of FIG. 7 gives a graph 701 of the distance from thechromaticity locus to the specified white-point, per wavelength. On thisgraph two minima may be noted at 703 and 704, corresponding tomonochromatic light which are considered cyan and yellow, respectively.Of all the monochromatic lights, cyan and yellow are considered the“most similar” to white, and therefore can be expected to have thesmallest distance to white in any color space where distance isproportional or approximately proportional to perceived difference incolor. On this plot, the region at 702 denotes the sub-band of lightbetween about 555 nanometers and about 600 nanometers, as previouslydescribed.

The optical density spectra of a set of standard dyes are plotted inFIG. 8. The term “standard dyes” herein refers to dye compounds that arecommonly used in absorptive ophthalmic lenses (e.g. sunglass lenses andother colored lenses), and is technically defined for the purposes ofthe present disclosure as any dye having a full-width-half-maximum(FWHM) width of greater than about 40 nanometers, as exemplified by thedye optical density spectra in FIG. 8 which all satisfy this property.In the present disclosure the optical density spectra data arenormalized to a maximum value of 1.0 at the wavelength of peakabsorptance. Conversion from normalized optical density to units ofphysical concentration (e.g. parts per million per millimeter) can bereadily performed by multiplication of the data by a linear scalingfactor. Such conversion depends on the dye strength, which may beobtained by simple experimentation or in many cases directly from themanufacturer's dye data sheet.

The standard dyes described herein are based on chemical pigments(including but not limited to anthraquinone, perinone, diazo, monoazo,rhodamine and others). The dyes can be obtained commercially fromKeystone Aniline Corporation of Chicago Ill. under the Keyplast™ brand,and can be incorporated into optical filters and/or ophthalmic lenses bya variety of methods including casting (e.g. cast acrylic), injectionmolding (e.g. using polycarbonate), or coating (e.g. polyurethane oracrylic coatings applied by a spin-on or dip process). Another processby which dye pigments can be incorporated into an ophthalmic lensinvolves immersion of the lens in a heated bath of fluid and pigment,wherein by diffusion the dye pigment molecules become embedded into theporous surface of a tintable hard-coat. The process is sometimes used inophthalmic processing labs to produce low-manufacturing volumecustom-tinted lens products. The resulting tints provide transmittancespectra substantially similar to the standard dyes described herein, andare commercially available from Phantom Research Laboratories of SanDiego, Calif. under the Opti-Safe™ brand, in addition to other vendors.Commercial providers of standard dyes also provide pre-mixedcombinations (blends) of standard dyes to form common colors. Forexample the color black requires a blend of several standard dyes tocreate a good approximation to the ideal neutral density filter.

In the present disclosure standard dyes are also comprehended to includephotochromic dyes, which are also available in a wide range of colorsand have similar broadband spectral transmittance properties (e.g. theReversacol™ brand of photochromic dyes which is manufactured by VivimedLabs Ltd. and distributed by Keystone Aniline Corporation). The behaviorof photochromic dyes is time-varying depending on the amount of ambientUV radiation, however such changes can be reasonably approximated byanalyzing the filter properties in two states: a first state where thephotochromic dye is not activated (i.e. the faded state), and a secondstate where it is activated according to average daylight (i.e. theexposed state), wherein a method of measuring the exposed state andfaded state of a lens comprising photochromic dyes is given by ANSIZ80.3-2010 section 5.7.

Referring again to FIG. 8, the optical density spectrum indicated at 801corresponds to a blue-absorbing dye, referred to as SD415Y in thepresent disclosure. The optical density spectrum indicated at 802corresponds to a blue-absorbing dye referred to as SD435Y in the presentdisclosure, and is commercially available under the brand name Keyplast™Yellow YC. The optical density spectrum indicated at 803 corresponds toa blue-green absorbing dye referred to as SD510R in the presentdisclosure, and is commercially available under the brand name Keyplast™Orange LFP. The optical density spectrum indicated at 804 corresponds toa yellow-green absorbing dye referred to as SD565P in the presentdisclosure. The optical density spectrum indicated at 805 corresponds tothat of a yellow-absorbing dye referred to as SD600V in the presentdisclosure. The optical density spectrum indicated at 806 corresponds tothat of a red-absorbing dye referred to as SD675B in the presentdisclosure. Dyes absorbing a particular color (e.g. yellow), when addedto an optical system cause the white-point to shift toward an opposingchromatic color (e.g. toward blue). The normalized optical density ofthe aforementioned dyes are tabulated in FIG. 26 using 5 nanometerintervals between 400 nanometers and 700 nanometers. The wavelengthsappear in the row under the heading “nm”, and the dye optical densityspectra under the headings enumerated above (e.g. SD415Y, etc.).

Examples of filters based on combinations of standard dyes that increasethe red-green separation factor (Ψ_(RG)) are described below along withFIG. 9 and FIG. 10. These examples were also selected to demonstrate theattainable limits on Ψ_(RG) in combination with target luminosity(τ_(v)) of greater than about 40%.

The transmittance spectra for a series of filters (referred tocollectively as the DCB series) are plotted in FIG. 9. The graph at 901corresponds to a filter with a luminous transmittance of about 40% andis referred to as DCB40 in the present disclosure. Referring to the setof standard dyes previously described, and their optical densitiesprovided in the table of FIG. 26, a dye formula for DCB40 can beexpressed as the formula:

DCB40=0.252×SD565P+0.599×SD600V

Wherein, in the above formula, the numbers 0.252 and 0.599 correspond toconcentrations of the dyes, and SD565P and SD600V correspond to thenormalized optical density spectra included in this formula (tabulatedin FIG. 26), and the code DCB40 corresponds to the mixture comprisingthe component dyes in the given proportions, wherein the units of thevector DCB40 are optical density and the transmittance of an opticalsystem comprising a filter composed of the given dye mixture is given bythe formula:

τ_(DCB40)=10^((−10×DCB40))

Returning to FIG. 9, the graph at 902 corresponds to a filter with about55% luminous transmittance and is referred to as DCB55 in the presentdisclosure, and has the dye formula:

DCB55=0.168×SD565P+0.399×SD600V

The graph at 903 corresponds to a filter with about 70% luminoustransmittance and is referred to as DCB70 in the present disclosure, andhas the dye formula:

DCB70=0.0839×SD565P+0.2×SD600V

The DCB series of filters have a blue color (i.e. impart a blue-tint towhite light passing through the filter), and provide a red-greenseparation factor between 0.7 and 0.8. Filters such as these generallymay be used to color ophthalmic lenses for aesthetic purposes, but thecolorimetric performance with respect to enhancement of red and greencolors is not significant. Transmittance spectra of the DCB series offilters are provided in 5-nanometer (nm) steps in the table of FIG. 27.

The transmittance spectra for another series of filters, referred tocollectively as the DCP series, are plotted in FIG. 10. These filtershave a pink-ish white point (i.e. impart a pink, reddish or purple-ishcolor to white light passing through the filter). These filters providered-green separation factors between 0.6 and 0.7. Filters withtransmittance curves similar to those depicted here may be marketed asoptical aids for color vision deficiency. The pink-ish color of suchfilters tends to disrupt the pseudo-isochromatic requirements in thedesign of vanishing-plate style color blindness screening tests (e.g.the Ishihara plate test, HRR plate test, etc.), however in practical useapplications they are often found to be either too dark, and/or noteffective enough.

Referring again to FIG. 10, the graph at 1001 corresponds to thetransmittance spectrum of a filter with about 40% luminous transmittanceand is referred to as DCP40 in the present disclosure, and has the dyeformula:

DCP40=1.07×SD565P

The graph at 1002 corresponds to the transmittance spectrum of a filterwith about 55% luminous transmittance and is referred to as DCP55 in thepresent disclosure, and has the dye formula:

DCP55=0.713×SD565P

The graph at 1003 corresponds to the transmittance spectrum of a filterwith about 55% luminous transmittance and is referred to as DCP70 in thepresent disclosure, and has the dye formula:

DCP70=0.357×SD565P

Transmittance spectra of the DCP series of filters are tabulated in5-nanometer (nm) steps in the table of FIG. 28.

The low performance of the DCB and DCP series filters provided above(which is quantifiable by noting their red-green separation factors lessthan 1.0) is a consequence of their component dyes, which are standarddyes having relatively broad spectral absorptance curves. Filters thatare preferable for increasing red-green color separation, and therebypotentially assisting an individual with some form of red-green colorblindness, should have a red-green separation factor that is greaterthan 1.0, or more preferably greater than 1.25, or more preferablygreater than 1.5. The broad-band absorptance of standard dyes result infilters with poor spectral selectivity. To provide filers withpreferable red-green separation factors requires the use of non-standardoptical materials.

One example of a non-standard absorptive optical material are certainrare-earth oxides, in particular neodymium oxide, which has acharacteristic absorption band between about 570 nanometers and about590 nanometers. A commercially available glass containing neodymiumoxide is referred to as ACE Blau and sold by Barberini SpA. Herein weanalyze the performance of the ACE Blau material in a range of opticalpath lengths, to better understand its properties with respect to thered-green separation factor performance metric. Referring now to FIG.11, the graph at 1101 corresponds to the ACE Blau glass at a thicknessof 1.8 millimeters. The corresponding filter is referred to herein asACE40. ACE40 provides a red-green separation coefficient of about 0.64and a luminous transmittance of about 40%. The graph at 1102 correspondsto the ACE Blau glass at a thickness of 1.2 millimeters. Thecorresponding filter is referred to herein as ACE55, and has a luminoustransmittance of about 55% and provides a red-green separation factor of0.75. The graph at 1103 corresponds to the ACE Blau glass at a thicknessof 0.6 millimeters. The corresponding filter is referred to herein asACE70, and has a luminous transmittance of about 70% and provides ared-green separation factor of 0.84. The ACE series of filters have ablue-gray color, i.e. the white-point tends toward blue but is lessstrongly tinted than the DCB series of filters described above. Whilethe coloration of these filters is preferable to that of the DCB and DCPseries described previously (because of its lower saturation), the ACEseries is not considered to have a strong enough effect on color visionto be marketed as an optical aid for color vision deficiency. Anunderlying issue with filters based on neodymium-oxide is the presenceof an absorptive band at around 520 nanometers, which degrades thequality of green colors in particular.

Transmittance spectra of the ACE series of filters are provided in5-nanometer (nm) steps in the table of FIG. 29.

Another example of a non-standard optical material are narrow-band dyes.We define narrow-band dyes herein to be dyes having an optical densityspectra with a FWHM of less than or equal to 40 nanometers around thewavelength of maximum absorption. Narrow-band dyes are based onproprietary organic chemical formulations. Narrow-band dyes arecommercially available from vendors including Exciton Inc of Dayton Ohioand Crysta-Lyn Chemical Company of Binghampton N.Y.

The plot shown in FIG. 12 shows the normalized optical density spectraof two dyes that both absorb yellow-light, one of which is a standarddye and the other a narrow-band dye. This plot illustrates thesignificant difference between standard dyes and narrow-band dyes. Thegraph at 1201 corresponds to the optical density of the dye SD600V,which is described previously. The dye SD600V has a FWHM of about 85nanometers. The graph at 1202 corresponds to the optical density of anarrow-band dye, referred to as NBD595 in the present disclosure. Thedye NBD595 has a FWHM of about 20 nanometers, which is significantlysmaller than that of the standard dye.

The normalized optical density spectra for a collection of narrow-banddyes are plotted in FIG. 13. These selected dyes represent only a smallfraction of commercial available dyes, however these were selected fromthose found to be most useful toward the formulation of filters foraffecting color vision in a desired manner. Other candidate dyes (forexample a dye with a peak absorption at about 565 nanometers) weretested by the authors, using the iterative methods described herein, andwere not found to be useful, i.e. the optimal formulas always concludedwith a zero concentration in the undesirable dye. The graph at 1301corresponds to the optical density spectrum of a narrow band dyereferred to herein as NBD405, and is commercially available under thebrand name Exciton ABS510. The graph at 1302 corresponds to the opticaldensity spectrum of a narrow band dye referred to herein as NBD425, andis commercially available under the name Exciton ABS527. The graph at1303 corresponds to the optical density spectrum of a narrow band dyereferred to herein as NBD475, and is commercially available under thename Exciton ABS473. The graph at 1304 corresponds to the opticaldensity spectrum of a narrow band dye referred to herein as NBD490, andis commercially available under the name Exciton P491. The graph at 1305corresponds to the optical density spectrum of a narrow band dyereferred to herein as NBD575, and is commercially available under thename Exciton ABS575. The graph at 1306 corresponds to the opticaldensity spectrum of a narrow band dye referred to herein as NBD595, andis commercially available under the name Exciton ABS595. The graph at1307 corresponds to the optical density spectrum of a narrow band dyereferred to herein as NBD670, and is commercially available under thename Exciton ABS668. Substitute dyes for the above commercial dyes canbe found in the Crysta-Lyn product catalog, and such substitutions arecomprehended by the present disclosure.

Normalized optical density spectra of the narrow-band dyes describedabove are provided in 5-nanometer (nm) steps in the table of FIG. 30.

Embodiments of filters that provide high red-green separation factors(i.e. greater than 1.0) in combination with high luminosity (i.e.,luminous transmittance greater than 40%) are described hereafter alongwith FIG. 14 and FIG. 15. These examples are filters comprising only asingle narrow-band dye component, which are readily designed by atrivial design process of simply modifying the single dye concentrationuntil the desired luminous transmittance is achieved.

FIG. 14 depicts the transmittance spectra for a series of filterscomprising only the dye component NBD595. The filters together arereferred to herein as the DMB series. The graph at 1401 corresponds to afilter referred to as DMB40 having a luminous transmittance of 40% and ared-green separation factor of 2.5. The formula for DMB40 is:

DMB40=4.31×NBD595

The graph at 1402 corresponds to a filter referred to as DMB55 having aluminous transmittance of about 55% and a red-green separation factor of1.97. The formula for DMB55 is:

DMB55=2.15×NBD595

The graph at 1403 corresponds to a filter referred to as DMB70 having aluminous transmittance of about 70% and a red-green separation factor of1.82. The formula for DMB70 is:

DMB55=1.08×NBD595

Transmittance spectra of the DMB series of filters are provided in5-nanometer (nm) steps in the table of FIG. 31.

The DMB series filters produce high amounts of red-green separationranging between 1.8 to 2.5. The darker embodiments (DMB40 and DMB55) maybe too dark for general indoor use as ophthalmic lenses. The lowspectral transmittance of such filters may also pose a hazard forgeneral use in eyewear: when the transmittance drops below the lesser ofabout 5%, or 1/10^(th) of the luminous transmittance (τ_(v)), at anypoint in the spectrum, the resulting filter may cause the appearance ofcertain artificial light sources to become too dark to ensure generalsafety. For example, yellow LED lights are often used as warningindicator lights (for example in traffic signals). Failure to see such alight due to filtering action in an ophthalmic lens is a safety concern.The lightest embodiment of this series (DMB70), causes only a smallreduction in overall luminosity (70% luminous transmittance) and has apreferable transmittance spectrum that complies with the minimumspectral transmittance needs as described. This particular embodimentwas tested in eyewear by the authors and found to be adequate for abroad range of typical indoor, low-light and night time applications,while also providing a significant improvement to red-green colorperception. An additional preferable property of the DMB series is thatthey have minimal to no effect on scotopic transmittance, in otherwords, night vision (as mediated by the rod cells) would be unaffectedby wearing a lens comprising such a filter. A less preferable propertyof the DMB series is their color, which is considered blue when vieweddirectly through the filter, however changes to a blue-violet hue whenthe path length is doubled due to a reflective object placed behind thelens. In particular, when incorporated into eyewear and worn on theface, the apparent color of the skin takes on a violet or lavender colorthat looks disturbing and unnatural. Preferable filters for use ineyewear should have a color appearance, that when worn on the face, areblue, pink, red, yellow, brown or gray. Therefore, a filter embodimentsuch as DMB70 could be a preferable choice when considering a filter forincorporated into an ophthalmic system where the coloration is notvisible to the outside observer: such as a contact lens or a spottingscope assembly.

The transmittance spectra for another series of filters, where thefilters consist of only a single narrow-band dye component, are shown inFIG. 15. The graph at 1501 corresponds to a filter referred to as DMP40having a luminous transmittance of 40% and a red-green separation factorof 2.28. The formula for DMP40 is:

DMP40=3.58×NBD575

The graph at 1502 corresponds to a filter referred to as DMP55 having aluminous transmittance of about 55% and a red-green separation factor of2.15. The formula for DMP55 is:

DMP55=1.83×NBD575

The graph at 1503 corresponds to a filter referred to as DMB70 having aluminous transmittance of about 70% and a red-green separation factor of1.98. The formula for DMP70 is:

DMP70=0.875×NBD575

Transmittance spectra of the DMP series of filters are provided in5-nanometer (nm) steps in the table of FIG. 32.

The DMP series have a color appearance usually described as pink: whenworn on the face in eyewear, in particular for the darker DMP40 andDMP55, the color appearance is unusually strong and is found to be notaesthetically pleasing.

The DMP70 filter and DMB70 filter are preferable for use in contactlenses, whereas use of a contact lens requires a high luminoustransmittance (e.g. at least 70%), and the aesthetic issues withcoloration as described are irrelevant. In addition, with respect to theapplication of a contact lens for assistance with protanomalous ordeuteranomalous color vision deficiency, the transmittance spectra ofthe DMB70 filter is preferable for use with deuteranomalous color visiondeficiency and the transmittance spectra of the DMP70 filter ispreferable for use with protanomalous color vision deficiency. Thispreference follows from the observation that 1) protanomalousindividuals experience a reduced sensitivity to long-wavelength visiblelight (i.e. red light) and 2) protanomalous individuals experience alower wavelength of unique yellow whereas deuteranomalous individualsexperience a longer wavelength of unique yellow and a higher sensitivityto longer wavelengths of light. A method for prescribing a contact lensto an individual with color vision deficiency may comprise firstconducting a color blindness test to determine their type and extent ofdeficiency, and then recommending an appropriate lens selected from thetwo contact lens alternatives having transmittance spectra substantiallyas described above. In another variation on the method just described, aspectacle lens can be recommended by a similar procedure, and whereasspectacle lenses may have a lower luminous transmittance (e.g. between40% and 60%), filters incorporated into such lenses may contain amixture of both NBD575 and NBD595 (or equivalent) narrow-band dyes. Inthese variations the method comprises recommending to thedeuteranomalous individual a lens containing an optical filtersubstantially similar to one of the CXB series filters (describedbelow), and/or to the protanomalous individual a lens containing anoptical filter substantially similar to one of the CXV series filters(also described below). A property shared by the CXB series filters isthat the transmittance of the filter at 575 nanometers is at least about2 times greater than the transmittance of the filter at 595 nanometers.A property shared by the CXV series filters is that the transmittance ofthe filter at 595 nanometers is at least about 2 times greater than thetransmittance of the filter at 575 nanometers.

Embodiments of filters comprising combinations of 2 or more dyesincluding at least one narrow-band absorbing dye are described in detailbelow along with FIG. 16, FIG. 17, FIG. 18, FIG. 19 and FIG. 20. Thedesign complexity of such filters increases with each additional dyeunder consideration (i.e., the number of possible metameric filterssatisfying the input chromaticity constraints is non-trivial), and sothe dye formulas of such filters are preferably optimized using theiterative methods described above along with FIGS. 1-4. The preferredconfiguration and variations of the design method are described alongwith these corresponding filter examples.

The transmittance spectra of a series of filters is shown in FIG. 16.These filters are referred to herein as the CXB series. The filterscomprise a combination of between 2 and 4 narrow-band dye components.The filters have a blue-green color (i.e. the white-point tends towardblue and also toward green). However, the provided colors are notstrong, appearing to also be substantially similar to gray. The seriesof filters includes embodiments having luminous transmittance betweenabout 40% and about 65%. The graph at 1603 corresponds to a filterreferred to herein as CXB40 having a luminous transmittance of 40% and ared-green separation factor of 1.72. The formula for CXB40 is:

CXB40=0.511×NBD670+0.557×NBD475+0.795×NBD575+1.29×NBD595

The graph at 1602 corresponds to a filter referred to herein as CXB55having a luminous transmittance of 55% and a red-green separation factorof 1.57. The formula for CXB55 is:

CXB55=0.251×NBD475+0.199×NBD575+1.29×NBD595

The graph at 1601 corresponds to a filter referred to herein as CXB65having a luminous transmittance of 65% and a red-green separation factorof 1.55. The formula for CXB65 is:

CXB65=0.167×NBD475 1.21×NBD595

Transmittance spectra of the CXB series of filters are provided in5-nanometer (nm) steps in the table of FIG. 33.

Optimized formulas for the CXB series (e.g. as disclosed above), wherethe corresponding optimized filters provide preferable red-greenseparation factors (greater than 1.0) and high luminous transmittance(greater than about 40%) may be produced by evaluating the describediterative design method using the red-green separation factor as thecolorimetric performance measure and a blue-green chromaticitycoordinate as the target white-point. Preferably the blue-greenchromaticity coordinate corresponds to hue between 10B and 5B and chromaof between 4 and 6 according to the Munsell color system.

The transmittance spectra of another series of filters is shown in FIG.17. These filters are referred to herein as the CXV series. The filterscomprise a combination of between 2 and 4 narrow-band dye components.The filters provide a white-point color considered a vermillion, whichis a gray color with a mild pink or purple tint. The series of filtersincludes embodiments having luminous transmittance between about 40% andabout 65%. The graph at 1703 corresponds to a filter referred to hereinas CXV40 having a luminous transmittance of 40% and a red-greenseparation factor of 1.3. The formula for CXV40 is:

CXV40=0.39×NBD475+0.557×NBD575+1.29×NBD595+1.39×NBD490

The graph at 1702 corresponds to a filter referred to herein as CXV55having a luminous transmittance of 55% and a red-green separation factorof 1.46. The formula for CXV55 is:

CXV55=0.195×NBD475+0.755×NBD575+0.724×NBD595+1.14×NBD490

The graph at 1701 corresponds to a filter referred to herein as CXV65having a luminous transmittance of 65% and a red-green separation factorof 1.48. The formula for CXV65 is:

CXV65=0.279×NBD475+0.795×NBD575

Transmittance spectra of the CXV series of filters are provided in5-nanometer (nm) steps in the table of FIG. 34.

Optimized formulas for the CXV series (e.g. as disclosed above), wherethe corresponding optimized filters provide preferable red-greenseparation factors (greater than 1.0) and high luminous transmittance(greater than about 40%) may be produced by evaluating the describediterative design method using the red-green separation factor as thecolorimetric performance measure and a purple or pink chromaticitycoordinate as the target white-point. Preferably the target white-pointcorresponds to hue of about 5P and chroma between 2 and 4 according tothe Munsell color system.

The transmittance spectra of another series of filters is shown in FIG.18. These filters are referred to herein as the CXN series. The filterscomprise a combination of 5 narrow-band dye components. The filtersprovide a white-point color considered to be neutral, or substantiallygray with little to no apparent coloration. The series of filtersincludes embodiments having luminous transmittance between about 14% andabout 40%. The graph at 1801 corresponds to a filter referred to hereinas CXN40 having a luminous transmittance of 40% and a red-greenseparation factor of 0.69. The formula for CXN40 is:

CXN40=0.43 1×NBD595+0.557×NBD475+0.755×NBD575+0.868×NBD670+1.64×NBD490

The graph at 1802 corresponds to a filter referred to herein as CXN25having a luminous transmittance of 25% and a red-green separation factorof 0.594. The formula for CXN25 is:

CXN25=0.862×NBD595+1.06×NBD475+1.11×NBD575+1.38×NBD670+2.53×NBD490

The graph at 1801 corresponds to a filter referred to herein as CXN15having a luminous transmittance of 15% and a red-green separation factorof 0.497. The formula for CXN15 is:

CXN15=1.03×NBD595+1.59×NBD475+1.67×NBD575+2.07×NBD670+3.79×NBD490

Transmittance spectra of the CXN series of filters are provided in5-nanometer (nm) steps in the table of FIG. 35.

Optimized formulas for the CXN series (e.g. as disclosed above), wherethe corresponding optimized filters provide strong color-enhancementeffects and a low luminous transmittance appropriate for incorporationinto sunglasses (less than 40%) may be produced by evaluating thedescribed iterative design method using a gamut-area based performancemetric. For example, the performance metric may be defined as the areaenclosed by a set of chromaticity coordinates corresponding to a set ofreference colors as seen through the filter, and the reference colorscorrespond to the Munsell color swatches used in the Farnsworth D-15 caparrangement test. The gamut area performance measure is described inU.S. patent application Ser. No. 14/014,991. Preferably the targetwhite-point corresponds to a chroma of less than 2 according to theMunsell color system.

The transmittance spectra of another series of filters is shown in FIG.19. These filters are referred to herein as the UVH series. The filterscomprise a combination of 3 narrow-band dye components and optionally 1standard dye component. The series of filters includes embodimentshaving luminous transmittance between about 35% and about 85%. The UVHseries of filters are designed to inhibit the transmission ofhigh-energy visible light (also called HEV light), which is a sub-bandof visible light where photons have the greatest energy, correspondingto wavelengths between about 390 nanometers and about 450 nanometers.The graph at 1901 corresponds to a commercially available HEV-blockingfilter known by the trade name BluTech. This filter is characterized bya nearly monotonic change in transmittance across the spectrum. The UVHseries of filters disclosed herein have complex spectral profiles thatare non-monotonic in transmittance per wavelength. The graph at 1902corresponds to a filter referred to herein as UVH415 having a luminoustransmittance of 85%. The formula for UVH415 is:

UVH415=0.227×NBD595+0.397×NBD425+1.57×NBD405

The graph at 1903 corresponds to a filter referred to herein as UVH430having a luminous transmittance of 75%. The formula for UVH430 is:

UVH430=0.322×NBD595+1.32×NBD425+2.09×NBD405

The graph at 1904 corresponds to a filter referred to herein as UVH450having a luminous transmittance of 35%. The formula for UVH450 is:

UVH450=1.4×NBD595+7.15×NBD425+9.95×NBD405+2.08×SD435Y

Transmittance spectra of the UVH series of filters are provided in5-nanometer (nm) steps in the table of FIG. 36.

The filter examples UVH415 and UVH430 provide filters with high luminoustransmittance and are adequate for general purpose eyewear intended forindoor use and night-time use. These filters have colors that aresubstantially neutral, which are preferable for aesthetic reasons. Inaddition, the configuration of notches in the spectral transmittance(e.g. at 510 nanometers and at 590 nanometers) provide a small butnoticeable increase to the quality of color vision.

The filter example UVH450 has a color that is considered yellow orbrown, and has a correlated color temperature of about 2700 Kelvin. Thefilter is preferable for incorporation into a sunglass lens, where itmay also be combined with a polarizing filter, and/or a photochromicdye. The spectral transmittance of the UVH450 example is less than 1%for all wavelengths from 400 nanometers to 450 nanometers, enabling theuse of the claim “UV450” for commercial advertising, which is related tothe term “UV400” which is defined by the industry to indicate a lensthat blocks at least 99% of light with wavelength of 400 nanometer orless. In another variation, the concentration of standard dye componentSD435Y may be reduced in the formula provided above, to yield a filterwith a lower protection rating, e.g. “UV425”, with the tradeoff that theresulting filter color may be preferable insofar as its saturation(chroma) is reduced. Preferably the filter color has a chroma of between2 and 4 according to the Munsell color system.

Optimized formulas for the UVH series (e.g. as disclosed above), wherethe corresponding optimized filters provide HEV light protection incombination with preferable filter color may be produced by evaluatingthe described iterative design method using the HEV attenuation factor,a colorimetric performance measure calculated by the formula

Ψ_(HEV)=((τ_(v)×((τ_(H)/τ_(L))−1))/(1−τ_(v))+1)

Wherein, in the above formula, m is the mean transmittance of the filterbetween about 390 nanometers and about 450 nanometers, T_(L) is the meantransmittance of the filter between about 450 nanometers and about 650nanometers, and τ_(v) is the luminous transmittance of the filter. Forsuch filters having a high luminous transmittance (e.g. greater than75%) the white-point preferably corresponds to a chroma of less than 2according to the Munsell color system. For such filters having a lowluminous transmittance (e.g. less than 40%) the white-point ispreferably within about 0.025 units of the black-body locus in the CIExy chromaticity space. The HEV attenuation factor of filter exampleUVH415 is about 6.1 and the red-green separation factor is about 0.47.The HEV attenuation factor of filter example UVH430 is about 6.2 and thered-green separation factor is about 0.35. The HEV attenuation factor offilter example UVH450 is about 44.2 and the red-green separation factoris about 0.25. The filter examples UVH415 and UVH430 provide awhite-point with low saturation, wherein the distance to the standardappearance of D65 at the (x, y) coordinates (0.31, 0.33) is at mostabout 0.025 units. The filter example UVH450 provides a white-point thatis substantially considered yellow and essentially transforms StandardIlluminant D65 (having a correlated color temperature of 6500 Kelvin) tothe color of Standard Illuminant A (having a correlated colortemperature of 2700 Kelvin).

The transmittance spectra of another series of filters is shown in FIG.20. These filters are referred to herein as the ACR series. The filterscomprise a combination of 2 narrow-band dye components and 1 standarddye component and optionally a neutral density absorber (such as a graydye mixture, a gray photochromic dye, or a gray polarizer). The ACRseries of filters are designed to inhibit the transmission of scotopiclight (light received by the rod cell photopigment), which are photonshaving a wavelength between about 450 nanometers and about 550nanometers. Filters that significantly limit the transmission ofscotopic light are often prescribed for individuals who suffer fromachromatopsia, a low-vision condition characterized by partial orcomplete lack of functioning cone cells. The limited scotopictransmission enables the wearer to use scotopic vision (i.e. nightvision) to see during typical indoor lighting and outdoor daylightconditions. One approach to meeting such needs would be to provide aneutral gray filter of the appropriate darkness, however this is lesspreferable compared to an orange or red filter that enables partialcolor vision. Cases of achromatopsia can be classified as eithercomplete achromatopsia (i.e. total loss of cone function) or incompleteachromatopsia (i.e. partial loss of cone function). For the latter case,a lens providing selective transmission is preferred. The graph at 2001corresponds to a conventional filter which may be prescribed by anophthalmologist for use indoors with achromatopsia. This filter has anorange color and a luminous transmittance of about 30%. The graph at2003 corresponds to a conventional filter which may be prescribed by anophthalmologist for use outdoors with achromatopsia. This filter has ared color and a luminous transmittance of about 8%. Such filters can bepurchased commercially, for example the orange-colored Filter #570 fromNoIR Medical Technologies Inc of South Lyon, Mich., and the red-coloredFilter #95 and Filter #99 also from NoIR Medical Technologies Inc ofSouth Lyon, Mich. The ACR series of filters shown here improve uponthese conventional designs by incorporating color-enhancing dyes (e.g.NBD595) which may provide better color vision to individuals withincomplete achromatopsia. The graph at 2002 corresponds to a filterreferred to herein as ACR25 having a luminous transmittance of 25%. Theformula for ACR25 is:

ACR25=0.167×NBD475+1.29×NBD595+1.81×SD510R

The graph at 2004 corresponds to a filter referred to herein as ACR10having a luminous transmittance of 10%. ACR10 employs the sameunderlying formula as ACR25 with the addition of a neutral-densityabsorber transmitting 40% of the light. For example, the absorber may bea neutral-density dye (e.g. typically a mixture of standard dyes to formgray and having a transmittance that is approximately constant perwavelength), preferably is a linear polarizer element, or is preferablya photochromic dye, or is more preferably a polarizing photochromic dye.

Transmittance spectra of the ACR series of filters are provided in5-nanometer (nm) steps in the table of FIG. 37.

The design of filters such as those in the ACR series are enabled by avariation on the iterative design method wherein the target white-pointconstraint is replaced by a scotopic transmittance constraint (i.e.apparent brightness according to the receptivity of the rod cellphotopigment). The substitution is appropriate since the extreme needsof the desired effect on color vision override any preference on thefilter color. The target scotopic transmittance is preferably less thanabout 10%, or is preferably less than about ⅓^(rd) of the luminoustransmittance of the filter. In combination with the modifiedconstraint, a measure of general color enhancement may be applied as thecolorimetric performance measure, for example a gamut-area based metricas described previously whereas gamut-area metrics are preferable in thedesign of dark (low luminous transmittance) filters, or the red-greenseparation factor may be used as a colorimetric performance measure todrive the optimal solution toward a filter that improves color vision.

FIG. 21 depicts a chromaticity diagram according to the CIE Yxy colorspace with respect to the CIE 1932 2-degree standard observer. Thedotted line at 2105 corresponds to the Planckian locus (or black-bodylocus) which is the curve in chromaticity space of an ideal black-bodyradiator having a temperature between 10000 Kelvin and 0 Kelvin. Filtersthat are preferable for integration into ophthalmic systems are thosehaving 1) not strongly colored tints, and 2) preferably colors which arenear the black-body locus. A region that satisfies these preferableproperties is indicated at 2111. The region spans the black-body locustemperatures from about 8000K to about 2700K. White-point colors fallinginto this region are substantially considered to be neutral inappearance, or mostly neutral but taking on a slight coloration. Thewhite-points of filter series CXN are indicated by the solid circlemarkers at 2107 which correspond to essentially gray or neutral colorswith a correlated color temperature of 6500K. The white-points of filterseries UVH are indicated by the open circle markers at 2106 and 2104,with 2106 corresponding to example UVH430 and the marker at 2104corresponding to example UVH450. The filter UVH430 has a substantiallyneutral appearance with a slight tint toward yellow. The filter UVH450takes on a stronger yellow (or brown) appearance and has a correlatedcolor temperature of about 2700K. A less preferable region of color isindicated at 2103 spanning correlated color temperatures of 2700K toabout 2000K, where filters in this region may be appear orange. Anotherregion that is less preferable for the color of filters is indicatedapproximately at 2115 corresponding to pink, purple and red colors withstrong coloration. The filter series ACR (ACR25 and ACR10) have awhite-point corresponding to the open square marker at 2109, which is ared color. The less preferable color is a necessary consequence of thescoptopic transmittance constraints. In another example, the filterseries DMP has corresponding white-points indicated by the uprighttriangles at 2113, with the most saturated marker corresponding to thefilter DMP40. These filters have a strong pink or purple color that isconsidered undesirable for aesthetic reasons. The CXV series of filtersalso have a white-point that tends toward pink, but are fully containedwithin the preferable region at 2111, wherein the diamond markers at2110 correspond to the white-points of these filters. Pink-ish orpurple-ish filters that are nearly gray are also called “vermillion”,especially in the eyewear industry. Another region in chromaticity spacethat is also less preferable (in particular for eyewear) is indicated at2116: this region corresponds to substantially blue-violet filters,which have an unusual appearance that is not preferred by mostconsumers. The filter series DMB has corresponding white-points in thisregion indicated by the inverted triangles at 2114. Whereas blue-ishfilters are preferred for achieving high red-green separation factorssimultaneously with high luminous transmittance, the chromaticity regionindicated at 2112 demarcates an area corresponding to blue-green colors,within which the white-points of the filter series CXB are contained andindicated by the solid square markers at 2108. The region 2101corresponds to strong green colors and the region 2102 to yellow-greencolors which are again less preferable than embodiments contained withinthe regions 2111 or 2112.

A scatter plot demonstrating the red-green separation factor (′PRG)versus luminous transmittance (τ_(v)) for the filter examples describedabove is shown in FIG. 22, corresponding data tabulated in FIG. 38 andFIG. 39. Neutral filters (equal transmittance at all wavelengths)provide a red-green separation factor of zero (for example shown by theinverted triangles at 2204 corresponding to neutral filters of 40%(ND40), 55% (ND55) and 70% (ND70) luminous transmittance. Analysis ofthis plot is useful to better understand how red-green separation factoras a colorimetric performance measure defines preferable properties offilters intended for use as optical aids for red-green color blindness,in particular for such filters rated as Category 1 lenses (which arenominally lenses having a luminous transmittance between about 40% andabout 80%). Category 1 lenses are not considered suitable as sunglasslenses. Category 1 lenses have a high enough luminosity that they may beusable under typical indoor lighting conditions, as well as low-lightsituations such as evening and night-time use. Filters such as the CXN25and CXN15 are found to have strong color enhancement effects, howeverare too dark for indoor use. The filter CXN40 has a luminoustransmittance corresponding to the lower limit for a Category 1 lens,however in subjective user testing was found to have only a mild effecton color perception, where CXV40 and CXB40 were found to have a strongeffect. We conclude that the red-green separation factor as colorimetricperformance measure is a reasonable choice for use with our iterativedesign method when the target luminosity is greater than about 40%. Theregion indicated at 2201 shows the preferable range of red-greenseparation factor versus luminous transmittance for Category 1 lenses,wherein the luminous transmittance is between about 40% and about 80%and the red-green separation factor is greater than 1.0. Preferably suchfilters provide a red-green separation factor greater than about 1.25,or greater than about 1.5, or greater than about 2.0. Preferably suchfilters provide luminous transmittance greater than about 50%, orgreater than about 60%. The region indicated at 2202 encloses filterdesigns having a luminous transmittance in the Category 1 range, butalso having red-green separation factor of less than 1.0, as describedpreviously (e.g. the ACE series, DCB, and DCP series). The regionindicated at 2203 encloses filter designs having a luminoustransmittance in the Category 2 range (comprising luminous transmittancefrom about 18% to about 40%) or having a luminous transmittance in theCategory 3 range (comprising luminous transmittance from about 8% toabout 18%). Category 2 lenses are considered medium sunglass lenses, andCategory 3 lenses are considered dark sunglass lenses.

The integration of dye-based filters into ophthalmic systems isaccomplished in a variety of methods that are known in the ophthalmiclens industry. An example of a possible ophthalmic system containing adye-based filter is shown in FIG. 23A, wherein the layers of anophthalmic system are depicted in a stacked arrangement. In this examplethe top layer (side of the lens furthest from the eye) is a hydrophobiccoating 23A01, the next layer is an anti-reflection coating 23A02 (whichitself comprises several layers), the next layer is the functionalcoating layer where the dye-based filter is contained, for example bydispersing of the dyes throughout an acrylate-based coating. Thefunctional coating is bonded to a lens substrate 23A04 using anysuitable method of attachment (spin-on, mold transfer, etc.). Thebackside of the lens substrate is then additionally coated with aback-side anti-reflection coating 23A05 and back-side hydrophobiccoating 23A06. The system described above is preferable for theformation of a prescription lens (a lens containing focusing power).Prescription lenses use variation in thickness across the surface of thelens to create optical power, however to maintain uniform spectralfiltering, the functional coating should maintain an approximatelyconstant thickness. Thus, integration of the dye components into thelens substrate is less preferable if the lens also function to createoptical power. In another variation, the lens may have zero power, orhave a reasonably low power (e.g. between +/−2 diopters), and in such avariation the filter dyes may be dispersed directly into the lenssubstrate 23A04, and the functional coating layer omitted 23A03. Inadditional variations, the functional coating may be applied on the backsurface of the lens substrate, or the component dyes may be distributedbetween both the lens substrate and a functional coating. In additionalvariations, the anti-reflection coatings and/or hydrophobic coatings maybe omitted. In further variations, the dyes may be dispersed into ahard-coat (anti-scratch coating) that is applied to both the front andback surfaces of the lens substrate. Another type of ophthalmic lens isa contact lens, wherein the dye solution may be integrated into the lenssubstrate, or into a region within the substrate, such that the dyecomponents are chemically bonded to the polymer forming the contactlens.

The integration of a dye-based filter into a lamp assembly is depictedin FIG. 23B. Herein the lamp assembly comprises an illuminant 23B05(e.g. an LED, incandescent filament or gas-discharge tube), abeam-forming lens 23B04, which may cast a narrow beam, wide beam orother spatial distribution of light, and a window that the beam of lightpasses through 23B02. Herein the filter component dyes are dispersedwithin the substrate forming the window. For improved efficiency thewindow may include anti-reflection coatings on the front 23B01 and back23B03 surfaces. In another variation, the component dyes may be appliedusing a functional coating (as described previously) directly on thesurface of the beam forming lens, instead of using a window. In anothervariation, the component dyes may be dispersed directly into the beamforming lens. In another variation the beam-forming lens may comprise amirror (e.g. a parabolic or ellipsoidal mirror), and the component dyesapplied as a functional coating on the surface of the mirror, and theconcentration of the dyes are reduced by about 50% to account for thedoubling of the effective path length. In some variations, only aportion of the light beam is filtered.

With respect to the integration of Category 1 filters (having luminoustransmittance between about 40% and about 80%) into eyewear, the reducedluminosity of the filter may present issues with visual obstruction tothe wearer in certain lighting conditions, especially in low-light ornight-time conditions. The issues can be alleviated by restriction ofthe application of the optical filter to a region within a lens. FIG.24A shows an example pair of eyewear where the lens 24A01 contains anear-field region at 24A02. In such an example the filter may be appliedas to only affect vision in the near-field region 24A02. Such anarrangement may be useful for eyewear intended for use where enhancedcolor vision is required for close-up task work, without obstructingvision generally. In another example, FIG. 24B shows an example pair ofeyewear where the lens is split into a near-field region at 24B02 and afar-field region at 24A01. In such an example the filter may be appliedas to only affect vision in the far-field region 24B02. Such anarrangement may be preferred when the eyewear is intended for useassistance with interpretation of colored signal lights (for example inmarine, automobile or aviation navigation) and where the signal lightsare primarily seen above the horizon line. In another variation thesplit between near-field and far-field regions is a continuous gradient,rather than a having a distinct line.

Figures included in this disclosure may be process flow diagrams thatvisually depict the flow of generalized objects and operations thatprocess and generate those objects. FIG. 25 depicts an example of aprocess flow diagram to aid in understanding the visual language. Inthis diagram, rounded boxes (e.g. at 2501 and 2503) depict objects,which may be understood as physical entities, virtual entities such asnumerical data, or composite objects containing a heterogeneousaggregation of component objects. A composite object containing ahomogeneous aggregation of objects is depicted by a rounded box with adouble-lined boundary, e.g. as shown at 2508 and 2511. A componentobject extracted from a composite object is depicted with a dottedarrow, e.g. as shown connecting entities 2501 and 2503. The flow ofobjects in the process is shown by a solid arrow, e.g. as shownconnecting entities 2501 and 2502. A squared box (e.g., at 2502 and2505) represents an operation. Operations may generate objects,transform objects or analyze objects. The outputs of an operation areshown by arrows pointing away from its box. The output of an operationis dependent on its inputs, which may be traced by following all arrowsleading into its box. Operations may be formed as a composite operationby encapsulating another process diagram, e.g. as shown at 2506. Thisconstruction enables process flow diagrams to be extended over multiplepages whereby a composite operation defined in one diagram may beinvoked by reference in another diagram. Operations may be connectedtogether in series or in parallel, the details of the order in whichspecific operations are performed is not necessarily defined by theprocess flow diagram syntax and must be inferred by accompanyingdescription. A double-lined arrow, e.g. as shown connecting 2508 and2509, represents iteration of the flow of a plurality of homogeneousobjects, and the process flow may be identified in accompanyingdescription using the phrase “for each . . . ”. Operations that areiterated are shown with a doubled-lined squared boundary, e.g. at 2509.An iterated operation varies its input with respect to each iteratedobject, but may hold constant inputs with respect to non-iteratedobjects, e.g. as shown along the flow arrow connecting 2507 and 2509.The process flow diagrams used in this disclosure are provided to aidunderstanding when interpreted along with the accompanying detaileddescription. The process flow diagrams used in this disclosure do notconstitute a formal specification for an algorithm but rather areillustrative devices provided to aid in understanding the accompanyingdescriptions.

The methods disclosed herein may be implemented, for example, on acomputer having a 2.3 GHz Intel Core i7 processor and 8 GB of RAM usingthe commercially available computational software program Mathematica®(including its linear program solvers) available from Wolfram Research,Inc. It should be understood by those of ordinary skill in the art,however, that the methods disclosed herein are not limited to the aboveimplementation and are independent of the computer/system architecture.Accordingly, the methods may equally be implemented on other computingplatforms, use other computational software (whether commerciallyavailable or coded specifically for the filter design methods), and alsomay be hard-wired into a circuit or other computational component.

This disclosure is illustrative and not limiting. Further modificationswill be apparent to one skilled in the art in light of this disclosure.For example, where methods and steps described above indicate certainevents occurring in certain order, those of ordinary skill in the artwill recognize that the ordering of certain steps may be modified andthat such modifications are in accordance with the inventions disclosedherein. Additionally, certain of the steps may be performed concurrentlyin a parallel process when possible, as well as performed sequentiallyas described above. Acts referred to herein as operations in a method orprocess may also be understood as “steps” in the method or process.Therefore, to the extent there are variations of the inventionsdisclosed herein, which are within the spirit of this disclosure orequivalent to the inventions disclosed herein, it is the intent thatthis disclosure and the claims it supports will cover those variationsas well. All publications and patent applications cited in thisdisclosure are incorporated herein by reference in their entirety as ifeach individual publication or patent application were specifically andindividually put forth herein.

1. An optical filter comprising one or more narrow-band dyes, whereinthe luminous transmittance of the filter is between 40% and 80%, thered-green separation factor of the filter is greater than 1.0, and theluminous transmittance of the optical filter is defined as the weightedphotopic transmittance of CIE Standard Illuminant D65 according to theCIE 1932 2-degree Standard Observer. 2-74. (canceled)
 75. The opticalfilter of claim 1, wherein the filter color is blue.
 76. The opticalfilter of claim 1, wherein the filter color is purple.
 77. The opticalfilter of claim 1, wherein the luminous transmittance of the filter isgreater than 50%.
 78. The optical filter of claim 75, wherein theluminous transmittance of the filter is greater than 50%.
 79. Theoptical filter of claim 76, wherein the luminous transmittance of thefilter is greater than 50%.
 80. The optical filter of claim 1, whereinthe red-green separation factor of the filter is greater than 1.25. 81.The optical filter of claim 75, wherein the red-green separation factorof the filter is greater than 1.25.
 82. The optical filter of claim 76,wherein the red-green separation factor of the filter is greater than1.25.
 83. The optical filter of claim 77, wherein the red-greenseparation factor of the filter is greater than 1.25.
 84. The opticalfilter of claim 78, wherein the red-green separation factor of thefilter is greater than 1.25.
 85. The optical filter of claim 79, whereinthe red-green separation factor of the filter is greater than 1.25. 86.An ophthalmic spectacle lens comprising the optical filter of claim 1,wherein the optical filter comprises two or more narrow-band dyes andfilters at least a 10 degree field of view.
 87. An ophthalmic spectaclelens comprising the optical filter of claim 75, wherein the opticalfilter comprises two or more narrow-band dyes and filters at least a 10degree field of view.
 88. An ophthalmic spectacle lens comprising theoptical filter of claim 76, wherein the optical filter comprises two ormore narrow-band dyes and filters at least a 10 degree field of view.89. An ophthalmic spectacle lens comprising the optical filter of claim77, wherein the optical filter comprises two or more narrow-band dyesand filters at least a 10 degree field of view.
 90. An ophthalmicspectacle lens comprising the optical filter of claim 78, wherein theoptical filter comprises two or more narrow-band dyes and filters atleast a 10 degree field of view.
 91. An ophthalmic spectacle lenscomprising the optical filter of claim 79, wherein the optical filtercomprises two or more narrow-band dyes and filters at least a 10 degreefield of view.
 92. An ophthalmic spectacle lens comprising the opticalfilter of claim 80, wherein the optical filter comprises two or morenarrow-band dyes and filters at least a 10 degree field of view.
 93. Anophthalmic spectacle lens comprising the optical filter of claim 81,wherein the optical filter comprises two or more narrow-band dyes andfilters at least a 10 degree field of view.
 94. An ophthalmic spectaclelens comprising the optical filter of claim 82, wherein the opticalfilter comprises two or more narrow-band dyes and filters at least a 10degree field of view.
 95. An ophthalmic spectacle lens comprising theoptical filter of claim 83, wherein the optical filter comprises two ormore narrow-band dyes and filters at least a 10 degree field of view.96. An ophthalmic spectacle lens comprising the optical filter of claim84, wherein the optical filter comprises two or more narrow-band dyesand filters at least a 10 degree field of view.
 97. An ophthalmicspectacle lens comprising the optical filter of claim 85, wherein theoptical filter comprises two or more narrow-band dyes and filters atleast a 10 degree field of view.